Department of Mathematicshttp://hdl.handle.net/10106/13522024-03-28T07:20:39Z2024-03-28T07:20:39ZA Support Vector Machine Based Cure Rate Model For Interval Censored DataPal, SuvraPeng, YBarui, SWang, Phttp://hdl.handle.net/10106/318252023-11-09T22:22:44Z2022-08-22T00:00:00ZA Support Vector Machine Based Cure Rate Model For Interval Censored Data
Pal, Suvra; Peng, Y; Barui, S; Wang, P
The mixture cure rate model is the most commonly used cure rate model in the literature. In
the context of mixture cure rate model, the standard approach to model the effect of covariates
on the cured or uncured probability is to use a logistic function. This readily implies that
the boundary classifying the cured and uncured subjects is linear. In this paper, we propose
a new mixture cure rate model based on interval censored data that uses the support vector
machine (SVM) to model the effect of covariates on the uncured or the cured probability (i.e.,
on the incidence part of the model). Our proposed model inherits the features of the SVM and
provides flexibility to capture classification boundaries that are non-linear and more complex.
Furthermore, the new model can be used to model the effect of covariates on the incidence part
when the dimension of covariates is high. The latency part is modeled by a proportional hazards
structure. We develop an estimation procedure based on the expectation maximization (EM)
algorithm to estimate the cured/uncured probability and the latency model parameters. Our
simulation study results show that the proposed model performs better in capturing complex
classification boundaries when compared to the existing logistic regression based mixture cure
rate model. We also show that our model’s ability to capture complex classification boundaries
improve the estimation results corresponding to the latency parameters. For illustrative purpose,
we present our analysis by applying the proposed methodology to an interval censored data on
smoking cessation.
S. Pal is with Department of Mathematics, University of Texas at Arlington, Texas, USA (email: suvra.pal@uta.edu).
Y. Peng is with Department of Public Health Sciences, Queen’s University, Kingston, Ontario, Canada
S. Barui is with Quantitative Methods and Operations Management Area, Indian Institute of Management,
Kozhikode, Kerala, India.
P. Wang is with Department of Mathematics, University of Texas at Arlington, Texas, USA
2022-08-22T00:00:00ZOPTIMAL CONTROL FRAMEWORKS FOR MODELING DYNAMICS AND ANDROGEN DEPRIVATION THERAPIES IN PROSTATE CANCERhttp://hdl.handle.net/10106/317772023-11-09T22:39:48Z2023-08-10T00:00:00ZOPTIMAL CONTROL FRAMEWORKS FOR MODELING DYNAMICS AND ANDROGEN DEPRIVATION THERAPIES IN PROSTATE CANCER
**Please note that the full text is embargoed until 08/01/2024** In this work, we present an optimal control approach for the assessment of treatments in prostate cancer. For this purpose, we use two different approaches, based on differential equations, to model the dynamics of prostate cancer. For the first approach, we use a system of ordinary differential equations (ODE) that model androgen-dependent and independent prostate cancer cell mechanisms. Given some synthetic patient data, we then performed a parameter estimation process by formulating an optimization problem to obtain the coefficients in this model. A second optimal control problem was formulated to obtain optimal androgen suppression therapies. A theoretical analysis of both optimization problems was performed to prove the existence of the minimizers. The numerical implementation of the optimization problems was done using a non-linear conjugate gradient method. Several numerical experiments demonstrate the accuracy and robustness of our proposed ODE framework. The second approach involved extending a reduced version of the aforementioned ODE model to a Liouville partial differential equation model that captures more variabilities and randomness involved in clinical trials and formulating the corresponding parameter estimation and optimal control problems. The numerical implementation was done using a second-order spatially accurate finite volume scheme. First, the comparison of the ODE and the Liouville framework results of parameter estimation demonstrated that the Liouville modeling framework is more accurate in capturing the cancer cell dynamics. Results of the Liouville optimal control framework demonstrated the effectiveness in obtaining optimal therapies to combat prostate cancer.
2023-08-10T00:00:00ZA Novel Regularized Orthonormalized Partial Least Squares Model for Multi-view Learninghttp://hdl.handle.net/10106/317402023-11-09T22:47:45Z2023-08-15T00:00:00ZA Novel Regularized Orthonormalized Partial Least Squares Model for Multi-view Learning
Over the past few years, the size of data dimensions or features has been increasing in various fields of science and engineering, owing to the rapid pace of data collection and the development of more advanced storage methods. However, to handle high-dimensional data, dimensionality reduction is essential before performing classification or regression tasks to eliminate noisy features. There are several numerical methods available for reducing data dimensionality, such as Canonical Correlation Analysis (CCA), Principal Component Analysis (PCA), and Linear Discriminant Analysis (LDA). While these methods offer valuable approaches to data dimensionality reduction, they do come with certain limitations. CCA, for instance, primarily focuses on finding correlations between two sets of variables, which might not fully capture the complexities of intricate relationships within multidimensional data. PCA, while excellent at preserving variance, can struggle to emphasize class separability when applied to classification tasks.
Acknowledging these limitations, this thesis introduces an innovative supervised dimensionality reduction algorithm that tackles both the reduction of data dimensionality and the concurrent classification of the data. Unlike conventional methods, this algorithm embarks on the dual task of revealing the projection matrix for dimension reduction alongside identifying the classifier hyperplane for data classification. The result is a model that excels in both accuracy and efficiency, enabled by its simultaneous learning of low-dimensional representation and classification models.
What distinguishes this proposed model is its versatility. It accommodates not only the dimensionality reduction and classification of single-view data but also extends its prowess to multi-view data. Through numerical simulations, the effectiveness and computational efficiency of the proposed model are showcased when contrasted against state-of-the-art methods in dimensionality reduction and classification.
A noteworthy feature of this novel approach is its capacity to generate two classifiers in tandem. This unique attribute widens its applicability across diverse classification experiments encompassing a variety of data types. In effect, the method’s dual-classifier capability amplifies its utility and establishes it as a versatile choice for tackling complex classification challenges.
2023-08-15T00:00:00ZLarge Eddy Simulation by using Wang’s Liutex-based subgrid modelhttp://hdl.handle.net/10106/317232023-11-09T22:51:05Z2023-08-09T00:00:00ZLarge Eddy Simulation by using Wang’s Liutex-based subgrid model
Turbulent flows and vortex structures in fluid dynamics have been captivating researchers for decades, owing to their intrinsic complexity and significance in various industrial and natural processes. Despite their fundamental importance, the definition and identification of vortices in turbulent flows continue to pose challenges, and to date, no universally accepted approach exists. This pursuit dates to the pioneering work of Hermann von Helmholtz in the 19th century, when the concept of vortices was first introduced.
In 2019, Liu et al. introduced a novel physical quantity termed "Liutex" in scalar, vector, and tensor forms, providing a promising avenue for understanding and characterizing turbulent flows. The Liutex approach offers a comprehensive framework for vortex identification, addressing issues that plagued previous methods and paving the way for more accurate simulations and analysis of turbulent flows. Building upon this foundation, our research seeks to explore the potential of Liutex in improving Large Eddy
v
Simulation (LES) techniques.
The primary objective of this study is to investigate the effectiveness of Wang's Liutex-based subgrid model for LES in capturing the intricate dynamics and structure of turbulent flows. The research methodology involves conducting extensive numerical simulations and data analysis using high-performance computing resources. The computational results are recorded and analyzed to study the mean velocity profile and flow characteristics.
Wang's Liutex-based subgrid model is implemented within the framework of LES, allowing for the representation of small-scale fluid motions such as eddies, swirls, and vortices. These subgrid-scale features are not fully resolved in LES, and subgrid models like Liutex are essential in bridging the gap between resolved and unresolved motions, improving the accuracy and predictive capabilities of the simulations. The new model will be tested in two LES coarse grid models, a LES that is 8 times more coarse than DNS and 32 times more coarse than DNS.
The research also explores the capability of Liutex to accurately identify and characterize vortices in turbulent flows. By quantitatively assessing vortex strength, rotational axes, vortex core locations, and sizes, the Liutex-based subgrid model offers insights into the underlying mechanisms of turbulent flows that were previously difficult to ascertain.
Additionally, the application of Liutex in LES enables the study of transitional flow regimes, where the transition from laminar to turbulent flow occurs. This aspect of the
vi
research expands the understanding of flow stability and transition mechanisms, which have significant implications in engineering applications and natural phenomena.
In conclusion, this study highlights the potential of the Liutex-based subgrid model as a powerful tool for enhancing Large Eddy Simulation of turbulent flows. By leveraging Liutex, researchers and engineers can gain a deeper understanding of the complex dynamics and structures present in turbulent flows, leading to improved predictive models and design strategies in various industrial and environmental applications. The findings of this research contribute to the advancement of fluid dynamics research and pave the way for more accurate and efficient simulations of turbulent flows in the future.
2023-08-09T00:00:00Z